2019/12/17 by Orlando Romero, Romero, Orlando, Mouhacine Benosman +1
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Sphingolipid Metabolism and Signaling #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.1912.08342
openalex publication_date 2019/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose two discontinuous dynamical systems in continuous\ntime with guaranteed prescribed finite-time local convergence to strict local\nminima of a given cost function. Our approach consists of exploiting a\nLyapunov-based differential inequality for differential inclusions, which leads\nto finite-time stability and thus finite-time convergence with a provable bound\non the settling time. In particular, for exact solutions to the aforementioned\ndifferential inequality, the settling-time bound is also exact, thus achieving\nprescribed finite-time convergence. We thus construct a class of discontinuous\ndynamical systems, of second order with respect to the cost function, that\nserve as continuous-time optimization algorithms with finite-time convergence\nand prescribed convergence time. Finally, we illustrate our results on the\nRosenbrock function.\n